VI. 6
5 D 7 5 7 5 5 8 6 9 6 5 sin`\cos`\tan`= a b \ c b \ a c = a@ b@ Step 5 5 5 5 5 4 5 4 sin`= Z Z = 5 cos`= Z Z = tan`= Z Z = 5 sin`= Z Z = cos`= Z Z = 5 tan`= Z Z = 5 Z=@+9@Z=5=5 sin`= Z Z = 9 5 = 5 cos`= Z Z = 5 = 4 5 tan`= Z Z = 9 = 4 Z=7@+9{7}@9=6=4 cos`= Z Z = 4 Z=6@-@=7= tan`= = tan`y= = /tan`+tan`y=+ = 4 4 D Z=7{49}@-4@9=5=5 Z=@-5@=44= /tan`= 5 5 tan`= Z = Z=\ =8 6 cos`= 6 Z = 5 Z=6\ 5 =0 /Z=0@-6@Z=64=8 7 sin`= Z 0 = 4 5 Step a@ 4 b@ 4 5 5 8 Z= 4 5 \0=6 /Z=0@-6@=44= /= \6\=96 8 tan`= Z = 6 8 7 96 8 5 5 4 7 5 9 4 0 5 Z= /Z=7@+9{}@9=6=6 /sin`= 6 =
9 sin`= 5 7 =90!Z=7 Z=5 Z=7@-5@=4=6 cos`= 6 7 tan`= 5 6 = 56 / cos` tan` = 6 7 _ 56 = 6 7 \ 56 = 4 5 06cos`-5=0cos`= 5 6 =90!Z=5Z=6 Z=6@-5@= sin`= tan`= 6 5 /0sin`\tan`=0\ 6 \ 5 = y= +6y y= +6y=0=0 {-40}{06} O OZ=4OZ=6 tan`a= 6 4 = -y+6=0 y -y+6=0 y=0=0 {-60}{0} O 6 5 7 y=#+6 a -y+6=0 OZ=6OZ=Z=6@+@=45=5 sina= 5 = 5 5 TDTD =D=D Dsin`= DZ Z a y O y O 5 4 TD y 6 =D= y TD D =D=y Z=@+6@=400=0 cos`= Z Z =6 0 = 4 5 cos`y= Z Z = 0 = 5 /cos`+cos`y= 4 5 + 5 = 7 5 5 DT /D== D DZ=6@+8@=00=0 D== sin`= Z DZ = 6 0 = 5 cos`= DZ DZ = 8 0 = 4 5 /sin`+cos`= 5 + 4 5 = 7 5 6 TED D 5 =DE= E Z=@+5@=69= /cos`= Z Z = 5 7 TED ED== 4 D ED E DEZ=7{49}@-@9=5 /tan`= DZ DEZ = 5 = 5 5 8 FZ=4@+4@= =4 Z=4@+4@+4@=48=4 /cos`= FZ Z = 4 4 = 6 6 8 D
9 FZ=@+6@=45=5 DFZ=@+6@+6@=8=9 cos`= FZ DFZ = 5 9 = 5 tan`= DZ FZ = 6 5 = 5 5 /cos`\tan`= 5 \ 5 5 = tan`7!= DZ ODZ = DZ =DZ=0.756 sin`0!\cos`90!=0\0=0 sin@`90!+cos@`0!=@+@= 0.599 0.857 0.5774 47! 45! 46! Step 6 sin`!=0.599 cos`!=0.857 tan`!=0.5774 sin`47!=0.74=47! cos`45!=0.707=45! tan`46!=.055=46! sin`60!+cos`0!= + = Step tan`45!+cos`60!=+ = - 4-4 5 0! 4 cos`45!\tan`60!= \= 6 sin`0!_tan`0!= _ = \ = cos`45!= Z = /Z= tan`45!= Z = /Z= 6 45! 7-8 9 7 4 0 96 8 60! 4 y=+ 5 y= + 6 y=-9 7 8 9 0.004 0.0598-6 4 5 6 7 -+tan` 8 0 9 85 0.9 0.608 0.7986 0.756 0 sin`7!= Z OZ = Z =Z=0.608 cos`7!= OZ OZ = OZ =OZ=0.7986 cos`0!\tan`60!= \= tan`0!+cos`60!=\ +\ =+= {sin`45!+cos`0!}{cos`45!-sin`60!} =[ + ][ - ] = 4-4 =- 4 4
{sin`60!-cos`60!} tan`60!+tan`45! =[ - ]_{+} = - + = {-}@ {+}{-} = 4- =- 4 80! =80!\ +4+5 =45! =80!\ 4 +4+5 =60! /sin`\cos`=sin`45!\cos`60! sin`45!= y = /y= \=6 /y=6\6=7 0D sin`45!= DZ 9 = /DZ= \9=9 D sin`60!= 9 Z = /Z=9\ =6 = \ = 4 5 4@-4+=0{-}@=0 /= sin`a= a=0!{?0!<a<90!} 6 5!<<60!0!<<0! /0!<-0!<90! cos`60!= -0!=60!=90! /=45! 7 sin`= =45!{?0!<<90!} /tan@`-5tan`+=tan@`45!-5tan`45!+ =@-5\+ =- 8 5!<<5!-05!<-<-5! /0!<05!-<90! tan`60!= 05!-=60!-=-45! /=5! /sin`\cos{60!-}=sin`0!\cos`45! = \ = 4 9 cos`45!= = /= \=6 D tan`45!= Z 8 = /Z=8 tan`60!= 8 Z = /Z=8\ = 8 D tan`60!= Z 6 = /Z=6 tan`0!= 6 +6 = +6=6\ =8 /= D cos`60!= 6 DZ = /DZ=6\= DD=60!-0!=0! D=D /=DZ= y=+6 a tan`a= tan`60!= a=60! 5
4 45! tan`45!= y y=+ 5 0! tan`0!= yk cos`90!-sin`90!=0-=- cos`90!-tan`45!+sin`0!=0-+0=- cos`0!\tan`0!-sin`90!\tan`60!+sin`60! =\ -\+ = -6+ 6 =- 6 tan`0!= k /k= \= y= + 6 y=a+b a=tan`60!= y=+b{-6} -6=\+b /b=-9 y=-9 7 sin`z=sin`y= Z Z = Z =Z 8 {OZZ} {ZOZ} {OZZ} {ZOZ} {ZDZ} 9 sin`54!= Z OZ =Z=08090 cos`54!= OZ OZ =OZ=0.5878 tan`54!= DZ ODZ =DZ=.764 /sin`54!+cos`54!-tan`54! {OZOZ} =0.8090+0.5878-.764=0.004 0O O=90!-!=58! sin`!= Z OZ =Z=0599 cos`58!= Z OZ =Z=0.599 /sin`!+cos`58!=0.599+0.599 =.0598 tan`0 4 sin`9!<sin`65! tan`47!<tan`48! sin`5!>sin`! tan`90!>tan`0! 5 sin`7!>cos`7! sin`90!>cos`90! 6 0!<<90!0<cos`< cos`+>0cos`-<0 /{cos`+}@+{cos`-}@ ={cos`+}-{cos`-} = 7 45!<<90!tan`> -tan`<0 /{-tan`}@=-{-tan`} =-+tan` 8 0!<<45!sin`<cos` sin`-cos`<0cos`-sin`>0 /{sin`-cos`}@-{cos`-sin`}@ =-{sin`-cos`}-{cos`-sin`} =0 9 sin`86!=0.9976cos`84!=0.045 tan`8!=8.44 =86y=84z=8 /-y+z=86-84+8=85 0sin`69!= 0 =0.96 /=96 cos`69!= y 0 =0.584 /y=.584 /+y=9.6+.584=.9 6
Step h h {-} h h + 85 5 =.08 y=.56 sin`58!= Z 0 Z=0`sin`58!=0\0.85=8.5 cos`58!= Z 0 Z=0`cos`58!=0\0.5=5. =90!-40=50! sin`50!= 4 =4sin`50!=4\0.77=.08 cos`50!= y 4 y=4cos`50!=4\0.64=.56 =90!-45!=45! Z=htan`45!=h\=h =90!-0!=60! Z=htan`60!=h\=h Z+Z=6 h+h=6{+}h=6 /h= 6 + = 6{-} {+}{-} ={-} =90!-45!=45! Z=htan`45!=h\=h =90!-60!=0! Z=htan`0!=h\ = h Z-Z= h- - h= h= /h= 6 - = 6{+} {-}{+} =+ =y= 6 =6sin`60!=6\ = Z=6cos`60!=6\ = Z=8-=5 y=75@+{9}@9=5 = Z=9sin`45!=9\ =9 =80!-{75!+45!}=60! Z= 9 sin`60! =9_ =9\ =6 4 5 8 = \8\6\sin`60! = \8\6\ = = \6\0\sin{80!-50!} = \6\0\sin`0! = \6\0\ =5 7
\\\sin`60!=4 \\\ =4 =4 /=8 5 6 0 D=4\6\sin`45! =4\6\ = D=8\8\sin{80!-50!} =8\8\sin`0! =8\8\ = D= \4\6\sin`60! = \4\6\ =6 D= \8\5\sin{80!-0!} = \8\5\sin`60! 8 60 `m 9 {+} 0 6 4{+}`cm@ 6`cm 45! 4 9`cm@ 5 8`cm@6`cm@ 6 `cm@ 7 `cm 8 5! 9 6`cm@ 0 6`cm@ 96`cm@ 7`cm@ 4`cm@ 4 5 `cm@ 5 `cm 6 7 `cm@ 7 0`cm@ 8 6`cm 9 50! =8sin`!=8\0.5=4.4 y=8cos`!=8\0.85=6.8 /+y=4.4+6.8=.04 =90!-4!=48! Z= cos`4! = sin`48! Z=6cos`60!=6\ ={cm} Z=6sin`60!=6\ ={cm} \p\@\=9p{cm#} = \8\5\ =0 4 Z=Z=6sin`45!=6\ =6{cm} \6\6\0=80{cm#} Step.04 `cm9p`cm# 4 80`cm# 5 8`m 6 `m 7 {0+0}m 8 `cm{6-}`cm 9 0 45 9 6 +6 4 5 6{6+} 6 {-} 7 00{-}`cm@ 5 Z= 9 sin0! =9_ =9\=8{m} 6 Z=0sin`9!=0\0.48=9.6{m} 9.6+.6=.{m} 7 0tan`0!+0tan`45!=0\ +0\ ={0+0}{m} 8
8 OZ O Z=6sin`0!=6\ ={cm} O OZ=6cos`0! O 0! 6`cm Z=77@+9{}@9=76=9 =80!-{75!+60!}=45! Z 45! 75! 6 60! =6\ Z=6sin`60!=6\ ={cm} OZ=6`cm OZ-OZ=6-{cm} = Z= sin`45! =_ =\ =6 9 Z 0 0! 8 Z=0sin`0!=0\ =5 Z Z=6cos`45! 6 60! 45! Z=0cos`0!=0\ =5 =6\ =6 Z=8-5= Z=75@+9{}@9=5 = 0 Z 0 Z=0sin`=0\ 4 0 5 =8 Z=0@-8@=6=6 Z=0-6=4 Z=8@+4@=80=45 Z 6 =80!-0!=60! 0! 60! 4 Z=6sin`60! =6\ = Z=6cos`60!=6\ = Z=4+=7 Z=6sin`45!=6\ =6 Z= 6 tan`60! = 6 = /Z=Z+Z=+6 4 Z Z=4sin`0!=4\ = 45! =80!-{05!+0!}=45! Z= sin`45! =_ =\ = 5 Z Z=cos`60! =\ =6 Z=sin`60!=\ =6 05! 0! 4 y 60! 45! 9
Z= 6 tan`45! = 6 =6 /=6+6 y= Z cos`45! =6_ =6\ =66 /y={6+6}\66=6{6+} 6 Z=h=45!=0! Z=htan`45!=h\=h Z=htan`0!=h\ = h 0Z=h =60! =60!=0! Z=htan`60!=h\=h Z=htan`0!=h\ = h Z= h- h= h= /h=\ =6 Z=6 h+ + h=6 h=6 /h= 8 + = 8{-} {+}{-} ={-} 7 Z=h`cm =60!=45! Z=htan`60!=h\ =h{cm} Z=htan`45!=h\=h{cm} Z=0`cm h`cm 0! 0`cm h+h=0{+}h=0 /h= 0 + = 0{-} {+}{-} =0{-} \0\0{-}=00{-}{cm@} 45! Z=h`cm =45!=0! Z=htan`45!=h\=h{cm} Z=htan`0!=h\ = h{cm} Z=4`cm h- h=4, - h=4 /h= - = {+} {-}{+} ={+} \4\{+}=4{+}{cm@} \Z\\sin`60!=9 \Z\\ =9 Z=9 /Z=6{cm} 8 =0!=60! Z=40tan`0!=40\ = 40 {m} Z=40tan`60!=40\=40{m} /Z=Z+Z = 40 9 Z=h 60 +40= {m} =60!=45! Z=htan`60!=h\=h Z=htan`45!=h\=h Z=6 h-h=6{-}h=6 /h= 6 - = 6{+} {-}{+} ={+} \4\6\sin`=6 sin`= /=45!{?0!<<90!} 4 ==75! =80!-{75!+75!}=0! \6\6\sin`0!= \6\6\ =9{cm@} 5 = \8\9\sin`45! = \8\9\ =8{cm@} 0
G= = \6\6+ \\9\ = \8 =6+7=6{cm@} =6{cm@} 6 =80!-{!+7!}=0! \6\8\sin{80!-0!} = \6\8\sin60! = \6\8\ 8`cm 6 8`cm 60! 8`cm 6\[ \8\8\sin`60!] =6\[ \8\8\ ] =96{cm@} ={cm@} 7 \0\Z\sin{80!-50!}=0 \0\Z\sin`0!=0 \0\Z\ =0 5 Z=0 /Z={cm} 8 \\8\sin{80!-}=4 48sin{80!-}=4 8 8\[ \6\6\sin`45!] =8\[ \6\6\ ] =7{cm@} =80!-5!=45! D=6\8\sin`45! =6\8\ 6`cm 45! 6`cm O sin{80!-}= =4{cm@} 90!<<80!0!<80!-<90! 80!-=45! =5! 9 D=+D 4 DDZ=Z=5`cm D=5\5\sin{80!-5!} =5\5\sin`45! =5\5\ = \4\4\sin`60! + \4\4\sin{80!-0!} = \4\4\ + \4\4\ = 5 {cm@} 5 =80!-0!=60! 8\Z\sin`60!=6 0D =+4 =6{cm@} DZ= 6 tan`45! = 6 =6{cm} DZ= 6 sin`45! =6_ =6\ ={cm} /D=D+D 8\Z\ =64\Z=6 /Z= 6 4 ={cm} 6 =D=0! D=4\7\sin{80!-0!} =4\7\sin`60! =4\7\ = \6\6+ \\9\sin`0! =4{cm@}
/O= 4 D = \4= 7 4 {cm@} 7 O O=80!-{40!+80!}=60! D 0`cm O 8`cm D= 40! 80! \0\8\sin`60! = \0\8\ =0{cm@} 8 5 \5\DZ\sin{80!-5!}= 5 \5\DZ\sin`45!= \5\DZ\ = 5 /DZ=6{cm}, 5 4 DZ= 5 9 \8\\sin{80!-}=4 sin{80!-}= 90!<<80!0!<80!-<90! 80!-=0! =50! 0 a c 0 DZ 0 b atan` sin` {csin`}@+{a-ccos`}@ a tan`-tan`y absin` acsin{80!-}
9 5 7 Z=5@-@= tan`= = 4 7 8 5 5 6 6 7 8 9 70! 0 {+}`cm@ 9 `cm@ 4 `cm 5 5.6`m 6 7`cm 7 66`cm 8 0{-}`m 9 6`cm@ 0 4`cm 4`cm@ 45! sin`= Z Z =5 Z tan`= 7 Z =5 8 / tan` sin` =5 8 _5 7 =5 8 \7 5 =7 8 5 y= 4 +4y=0=0 {-0}{04} OZ=OZ=4 Z=@+4@=5=5 /cos`a= OZ Z = 5 6 EGZ=\a=a EZ=\a=a EGGE=90! sin`= GZ EZ = a a = = cos`= EGZ EZ =a a = = 6 tan`= GZ EGZ = a a = = /sin`\tan`+cos`= \ + 6 = 6 6 + 6 sin`= 4 5 =90!Z=5Z=4 Z=5@-4@ =9= 5 4 = 6 6 = 6 7 sin`60!+ cos`45! -tan`0! =\ + \ -\ cos`= 5 tan`= 4 = + -= /cos`+tan`= 5 + 4 = 9 5 +0 5 =9 5 T == Z=5@+@=69= sin`= Z Z = 5 Z cos`= Z = /cos`-sin`= - 5 = 7 4 TED =DE= Z=7@-8@=5=5 8 sin`60!+cos`0!= + = tan`45!= /sin`60!+cos`0!=tan`45! tan`60!\sin`0!=\ = cos`60!= /tan`60!\sin`0!=cos`60! 9 40!<<0! 0!<-40!<90! cos`60!=
sin{-40!}= -40!=0! /=70! 0 Z= tan`0! =_ =\ ={cm =45! Z=Z=`cm /= \{+}\ 5=90!-5!=8! Z=0tan`8! =0\0.78 =5.6{m} 6 Z Z=8sin`0! 8`cm 0! 6`cm ={+}{cm@} =8\ =4{cm sin`= DZ ODZ = DZ =DZ cos`= OZ ODZ = OZ =OZ sin`z= OZ OZ = OZ sin`z=sin`y= OZ ODZ = OZ =OZ tan`z= OZ Z = Z 0!<<45! sin`+cos`>0sin`-cos`<0 {sin`+cos`}@-{sin`-cos`}@= {sin`+cos`}+{sin`-cos`}= sin`=sin`= /=0!{?0!<<45!} /tan`=tan`0!= ==0!=60! Z=6sin`60!=6\ ={cm} Z=6cos`60!=6\ ={cm} 9 \\= {cm@} 4DZ=4\=4{cm} /Z= DZ= \4={cm} O OZ=tan`45!=\={cm} Z=8cos`0!=8\ =4{cm} Z=6-4={cm} Z=7{9}@+4@9=8=7{cm} 7 Z 60! Z=8sin`45! =8\ 75! 8`cm =9{cm} =80!-{75!+45!}=60! Z= 9 sin`60! =9_ =9\ =66{cm} 8 h`m Z 45! Z=h`m 0! 40`m =45!=60! Z=htan`45!=h\=h{m} Z=htan`60!=h\=h{m} Z=40`m h+h=40{+}h=40 /h= 40 + = 40{-} {+}{-} =0{-} 0{-}`m 9=80!-{0!+0!}=0! =Z=Z=8`cm 45! 4
\8\8\sin{80!-0!} = \8\8\sin`60! = \8\8\ =6{cm@} 0 \9\Z\sin{80!-5!}=9 \9\Z\sin`45!=9 \9\Z\ =9 9 4 Z=9 /Z=4{cm} cos`= Z 0 = 5 /Z= 5 \0=4{cm} Z=0@-4@=84={cm} \4\=4{cm@} \5\8\sin`=0 60sin`=0 sin`= /=45!{?0!<<90!} 5